Such a shaving apparatus is known from U.S. Pat. No. 4,168,570. In the known apparatus the skin supporting rim is formed by the edge of the opening of the holder in which the cutting units are mounted. The skin supporting rim serves for slightly tautening the skin before the external cutting member is moved over the skin. Thus, it is achieved that the hairs to be severed are better erected so that they can be severed better and closer to the skin. An even more important function of the skin supporting rim is to support the skin around the external cutting member. This ensures that the pressure on the external cutting member does not become too high. An excessive pressure leads to skin injury and irritation because the skin then penetrates further into the hair-entry apertures and can come into contact with the internal cutting member. The external cutting member is mounted in the holder so as to allow movement in, preferably, any direction. As a result, the shaving surface, which is formed by the outer surface of the external cutting member facing the skin, can readily adapt itself to the shape of the facial area to be shaved. The maximum permissible tilting angle of the external cutting member, is determined by the length over which the external cutting member projects above the skin supporting rim. A large projection length gives rise to large pressure peaks on the peripheral parts of the external cutting member because the skin supporting rim cannot properly support the skin. As already stated above, a higher pressure leads to skin injury and irritation. When the external cutting member is tilted relative to its associated skin supporting rim, this rim cannot perform its skin supporting function in an optimum manner because this skin supporting rim is situated further from the shaving surface of the external cutting member. Moreover, large undesirable pressure peaks are produced on that part of the external cutting member which has the largest projection length.